What is the vertex form of #y= 3x^2 - 14x - 10 #?

1 Answer
Mar 16, 2018

#y=3(x-7/3)^2-79/3#

Explanation:

#"the equation of a parabola in "color(blue)"vertex form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))#

#"where "(h,k)" are the coordinates of the vertex and a"#
#"is a multiplier"#

#"to obtain this form use the method of "color(blue)"completing the square"#

#• " the coefficient of the "x^2" term must be 1"#

#rArry=3(x^2-14/3x-10/3)#

#• " add/subtract "(1/2"coefficient of x-term")^2" to"#
#x^2-14/3x#

#rArry=3(x^2+2(-7/3)xcolor(red)(+49/9)color(red)(-49/9)-10/3)#

#color(white)(rArry)=3(x-7/3)^2+3(-49/9-10/3)#

#color(white)(rArry)=3(x-7/3)^2-79/3larrcolor(red)"in vertex form"#